2a^2-5=9a

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Solution for 2a^2-5=9a equation:


Simplifying
2a2 + -5 = 9a

Reorder the terms:
-5 + 2a2 = 9a

Solving
-5 + 2a2 = 9a

Solving for variable 'a'.

Reorder the terms:
-5 + -9a + 2a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-5 + -9a + 2a2 = 0

Factor a trinomial.
(-1 + -2a)(5 + -1a) = 0

Subproblem 1

Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5

Subproblem 2

Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5

Solution

a = {-0.5, 5}

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